Which Is A Correct Statement About The Description two Less Than The Quotient Of A Number Cubed And Nine, Increased By Twelve When N = 3 N=3 N = 3 ?Select The Three Correct Answers.

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Introduction

In this discussion, we will analyze the given description "two less than the quotient of a number cubed and nine, increased by twelve" when n=3n=3. We will evaluate the statement and identify the correct answers.

Breaking Down the Description

The description can be broken down into several steps:

  1. Number cubed: The number nn is cubed, which means it is raised to the power of 3. In this case, n=3n=3, so the cubed value is 33=273^3 = 27.
  2. Quotient of the cubed value and nine: The quotient is obtained by dividing the cubed value by 9. So, we have 27÷9=327 \div 9 = 3.
  3. Two less than the quotient: We subtract 2 from the quotient, which gives us 3−2=13 - 2 = 1.
  4. Increased by twelve: Finally, we add 12 to the result, which gives us 1+12=131 + 12 = 13.

Evaluating the Statement

Now that we have evaluated the description, let's consider the statement. The statement is likely to be in the form of a mathematical expression or an equation. We need to identify the correct answers based on the evaluated description.

Possible Correct Answers

Based on the evaluated description, the possible correct answers are:

Answer 1

The correct statement is: "The value of the expression is 13 when n=3n=3."

Answer 2

The correct statement is: "The expression can be simplified to 1+121 + 12 when n=3n=3."

Answer 3

The correct statement is: "The value of the expression is 13 when n=3n=3, and it can be obtained by evaluating the expression step by step."

Conclusion

In conclusion, the correct answers to the statement about the description "two less than the quotient of a number cubed and nine, increased by twelve" when n=3n=3 are:

  • The value of the expression is 13 when n=3n=3.
  • The expression can be simplified to 1+121 + 12 when n=3n=3.
  • The value of the expression is 13 when n=3n=3, and it can be obtained by evaluating the expression step by step.

These answers are based on the evaluated description and provide a clear understanding of the statement.

Step-by-Step Solution

Here's a step-by-step solution to the problem:

  1. Evaluate the cubed value of the number: n3=33=27n^3 = 3^3 = 27
  2. Calculate the quotient of the cubed value and nine: 27÷9=327 \div 9 = 3
  3. Subtract 2 from the quotient: 3−2=13 - 2 = 1
  4. Add 12 to the result: 1+12=131 + 12 = 13

Mathematical Expression

The mathematical expression for the given description is:

n39−2+12\frac{n^3}{9} - 2 + 12

When n=3n=3, the expression can be evaluated as follows:

339−2+12=13\frac{3^3}{9} - 2 + 12 = 13

Simplifying the Expression

The expression can be simplified by following the order of operations (PEMDAS):

  1. Evaluate the cubed value of the number: n3=33=27n^3 = 3^3 = 27
  2. Divide the cubed value by 9: 27÷9=327 \div 9 = 3
  3. Subtract 2 from the result: 3−2=13 - 2 = 1
  4. Add 12 to the result: 1+12=131 + 12 = 13

The simplified expression is:

1+12=131 + 12 = 13

Final Answer

The final answer to the problem is:

  • The value of the expression is 13 when n=3n=3.
  • The expression can be simplified to 1+121 + 12 when n=3n=3.
  • The value of the expression is 13 when n=3n=3, and it can be obtained by evaluating the expression step by step.

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Q: What is the correct statement about the description "two less than the quotient of a number cubed and nine, increased by twelve" when n=3n=3?

A: The correct statement is: "The value of the expression is 13 when n=3n=3." This is because when we evaluate the expression step by step, we get 1+12=131 + 12 = 13.

Q: How do I evaluate the expression "two less than the quotient of a number cubed and nine, increased by twelve" when n=3n=3?

A: To evaluate the expression, follow these steps:

  1. Evaluate the cubed value of the number: n3=33=27n^3 = 3^3 = 27
  2. Calculate the quotient of the cubed value and nine: 27÷9=327 \div 9 = 3
  3. Subtract 2 from the quotient: 3−2=13 - 2 = 1
  4. Add 12 to the result: 1+12=131 + 12 = 13

Q: Can the expression "two less than the quotient of a number cubed and nine, increased by twelve" be simplified?

A: Yes, the expression can be simplified by following the order of operations (PEMDAS):

  1. Evaluate the cubed value of the number: n3=33=27n^3 = 3^3 = 27
  2. Divide the cubed value by 9: 27÷9=327 \div 9 = 3
  3. Subtract 2 from the result: 3−2=13 - 2 = 1
  4. Add 12 to the result: 1+12=131 + 12 = 13

The simplified expression is:

1+12=131 + 12 = 13

Q: What is the final answer to the problem?

A: The final answer to the problem is:

  • The value of the expression is 13 when n=3n=3.
  • The expression can be simplified to 1+121 + 12 when n=3n=3.
  • The value of the expression is 13 when n=3n=3, and it can be obtained by evaluating the expression step by step.

Q: How do I apply the order of operations (PEMDAS) to the expression?

A: To apply the order of operations (PEMDAS), follow these steps:

  1. Evaluate the cubed value of the number: n3=33=27n^3 = 3^3 = 27
  2. Divide the cubed value by 9: 27÷9=327 \div 9 = 3
  3. Subtract 2 from the result: 3−2=13 - 2 = 1
  4. Add 12 to the result: 1+12=131 + 12 = 13

Q: What is the significance of the order of operations (PEMDAS) in evaluating the expression?

A: The order of operations (PEMDAS) is crucial in evaluating the expression because it ensures that the operations are performed in the correct order. Without following the order of operations, the expression may be evaluated incorrectly, leading to an incorrect result.

Q: Can I use a calculator to evaluate the expression?

A: Yes, you can use a calculator to evaluate the expression. However, it's essential to understand the steps involved in evaluating the expression and the order of operations (PEMDAS) to ensure that the result is accurate.

Q: How do I check my work when evaluating the expression?

A: To check your work, follow these steps:

  1. Evaluate the cubed value of the number: n3=33=27n^3 = 3^3 = 27
  2. Calculate the quotient of the cubed value and nine: 27÷9=327 \div 9 = 3
  3. Subtract 2 from the quotient: 3−2=13 - 2 = 1
  4. Add 12 to the result: 1+12=131 + 12 = 13

Verify that the result is correct by plugging in the values into the expression and evaluating it step by step.

Q: What if I make a mistake when evaluating the expression?

A: If you make a mistake when evaluating the expression, don't worry! Mistakes are an opportunity to learn and improve. Review the steps involved in evaluating the expression and the order of operations (PEMDAS) to ensure that you understand the process correctly. If you're still unsure, ask for help or consult a resource to clarify the concept.